Semantics-Based Verification of an Implemented Shor Oracle for ECDLP in Qrisp

2026-05-01

AI Summary

This work addresses the vulnerability of Shor’s algorithm for the elliptic curve discrete logarithm problem (ECDLP) to subtle implementation deviations in the group operation oracle, which can invalidate its underlying mathematical model. For the first time, semantic auditing is introduced into ECDLP quantum software development: leveraging the Qrisp framework, the authors construct a compilable implementation that formally specifies oracle behavior through program semantics, derives refinement verification obligations for critical components, and performs end-to-end validation against classical reference implementations. The study not only confirms the consistency of the core point-update primitive with classical counterparts under well-formed inputs but also uncovers semantic discrepancies in existing toolchains—specifically, controlled executions violating expected control laws. These findings establish semantic auditing as an essential prerequisite for building trustworthy ECDLP quantum software.

Abstract

Shor-style quantum algorithms for the elliptic-curve discrete logarithm problem (ECDLP) are highly sensitive to the exact semantics of their group-operation oracles. Consequently, minor implementation choices can invalidate the intended mathematical model and lead to misleading conclusions. This paper introduces a semantics-first verification perspective for an end-to-end, compilable ECDLP implementation built on Qrisp. We specify the implemented oracle at the level of program semantics, derive refinement-style verification obligations for its key components, and provide a high-level complexity argument for the resulting oracle family. A small case study highlights that (i) the core point-update primitive agrees with a classical reference on well-formed inputs, yet (ii) controlled execution may violate the expected control law under the evaluated toolchain, despite a passing trivial control sanity check. These results position semantic auditing as a practical prerequisite for trustworthy ECDLP-oriented quantum software.

Problem

• ECDLP
• quantum oracle
• program semantics
• verification
• Shor's algorithm

Innovation

• semantics-based verification
• Shor oracle
• ECDLP
• quantum software validation
• refinement-style verification